In a producing of a carbon fiber or the like, as a precursor, for example, a fiber bundle made of a polyacrylonitrile polymer is employed as a fiber, and the fiber bundle is required to be excellent in a strength and a degree of orientation. Such a fiber bundle can be obtained, for example, by fiber spinning a fiber spinning solution including a polyacrylonitrile polymer so as to form a coagulated fiber, obtaining a densified fiber bundle by drawing in a bath and drying the coagulated fiber, and thereafter carrying out a secondary drawing treatment of the fiber bundle under a pressure steam atmosphere.
In the treatment of the fiber bundle under the pressure steam atmosphere, there is used a treatment apparatus which makes the fiber bundle travel inside of the apparatus and supplies a pressure steam with respect to the fiber bundle. In such a treatment apparatus, if the pressure steam supplied to the inside of the apparatus leaks out in large quantities to the outside of the apparatus from an inlet and an outlet of the fiber bundle, a pressure, a temperature, a humidity and the like in the inside of the apparatus becomes unstable, and there has been a case that a fuzz, a broken thread or the like is generated in the fiber bundle. Further, a lot of pressure steam is necessary for suppressing an influence of the leakage of the pressure steam to the outside of the apparatus, and an increase of an energy cost has been caused.
As a treatment apparatus which suppresses the leakage of the pressure steam from the inside of the apparatus, for example, Japanese Patent Application Laid-Open No. 2001-140161 (Patent Document 1), discloses a pressure steam treatment apparatus which is provided with a pressure steam treatment chamber which treats a fiber bundle traveling in a fixed direction by a pressure steam, and two labyrinth sealing chambers which extend from front and rear sides of the pressure steam treatment chamber. The labyrinth sealing chamber is provided with labyrinth nozzles in multiple stages in parallel along a fiber bundle travel path, the labyrinth nozzles being configured from plate pieces extending perpendicularly toward the fiber bundle from inner wall surfaces of a top plate and a bottom plate which are opposed to each other. An energy is consumed at a time of passing through each of spaces (expansion chambers) between the labyrinth nozzles, whereby an amount of leakage of the pressure steam is lowered.
According to the Patent Document 1, the first and second labyrinth sealing chambers are arranged in the front and rear sides of the pressure steam treatment chamber, and a plurality of fiber bundles traveling in parallel like a sheet along the fiber bundle travel path are treated under the pressure steam atmosphere in a lump. A value of a ratio (L/P) between an extension length L of the labyrinth nozzle from the inner wall surfaces of the top plate and the bottom plate, and a pitch P between the front and rear nozzles is between 0.3 and 1.2, and a number of the stages of the labyrinth nozzles is set to 80 to 120 in both of a first and a second labyrinth sealing chambers in the front and rear sides. Further, a filling factor F of the fiber bundle calculated by the following expression in the fiber bundle travel path within the labyrinth sealing chamber is set to 0.5 to 10%.filling factor F={K/(ρ×105)}/A 
Here, K: fiber bundle fineness (tex)                ρ: fiber bundle density (g/cm3)        A: opening area of the fiber bundle travel path (cm2).        
Since a magnitude of an expansion chamber formed between the front and rear nozzles comes to a preferable one by setting the value of L/P to the range, and it is possible to extremely consume the energy by repeating generation and elimination of a small eddy current of a rotation within the expansion chamber, a decompression effectively makes progress. It is possible to effectively suppress a team leakage amount in cooperation with the number of the forming stages of the labyrinth nozzles such as 80 to 120 stages, and it is possible to effectively prevent a damage of the fiber bundle and the fuzz.